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Unformatted text preview: Problem Set 4: Problem 3. Problem: A piston of mass m and cross-sectional area A is initially in equilibrium at the center of a cylinder under pressure p . The cylinder is closed at both ends. The piston is moved to the left a distance 1 2 d and released. Because the gas in the cylinder is a perfect gas, we know that the pressure varies inversely with volume. Ignoring friction between the piston and the cylinder, determine the pistons velocity when it returns to the center of the cylinder. Express your answer in terms of m , d , p and A . Solution: Because we are dealing with a perfect gas, we know that pV = constant . Before the piston is displaced, the volume of each chamber is V = Ad . Therefore, the pressure is given by pV = pAd When the piston is displaced, the pressure on its left surface, p L , and on its right surface, p R , are as shown in the figure. p L p R x 2 d x ...... ...... ...... .........
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